The teams, who had shared 12 goals in their last two matches, cancelled each other out as the hosts squandered the chance to move clear in second place.
Motherwell leapfrogged the Highlanders with their 2-1 win at home to leaders Celtic, while United moved above Aberdeen to within one point of the top six.
Jon Daly had a golden opportunity to open the scoring midway through the first half but he headed Willo Flood's cross wide from close range.
At the opposite end Billy McKay forced the first meaningful save from Radoslaw Cierzniak. The Northern Irishman's header from the edge of the box came from an Aaron Doran cross.
Andrew Shinnie might have made the breakthrough in the final minute of the half but his volley from the edge of the area was turned wide by Cierzniak.
Daly headed over a Flood free-kick from six yards just before the hour, then Andrew Shinnie's low shot from a Doran cross was saved well by Cierzniak as the end-to-end battle continued.
Cierzniak denied Andrew Shinnie once more when the Scotland international pounced on a Doran cross, but his header was saved comfortably.
Ryan Esson excelled 12 minutes from time with a smart save. John Rankin's shot from the edge of the area was deflected off Daly en route to goal - but the stopper reacted smartly to grasp the ball on the line.
Caley Thistle club captain Richie Foran replaced Billy McKay to make his return from a knee injury, which had him sidelined for the last four weeks, with nine minutes to go. The Irishman forced a late save from Cierzniak when he connected with a David Raven cross.
- Sports & Recreation
- Andrew Shinnie
- Willo Flood